I have a long and winding path > duplicated > and I now want to break it up into several sections that I'll convert to arrows that parallel the original path.

I've successfully broken the path into sections, but they appear to remain a single object. I want to now move them as independent objects. How do I do this?

Break apart?

Hi.

You can break apart compound paths with the break apart option (Ctrl+Shift+K) to single paths.
As you want to have the original path to be broken apart to it's segments,
you would need to edit at least two duplicants of the original path before the breaking apart option would do that job.
On one duplicant, you would need to unconnect the 1st and 2nd, the 3rd and 4th, ... nodes,
on the other duplicant unconnect the 2nd and 3rd, the 4th and 5th, and so on nodes.
Then by breaking apart theose, you would get paths showing each of the original's segments.

If you want arrows along the path parallel to it, you could try the pattern along path live path effect.
Press Shift+Ctrl+7 for the lpe panel,
select a previously drawn arrow (pointing to the right) and copy it, then select the original path and select the pattern along path in the lpe panel.
Paste the pattern, chose repeated, stretched settings, and add some normal offsetting.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Paths-LivePathEffects-PatternAlongPath.html

Thanks; really useful.

Because I'm eventually making a 'cartoon' from multiple .png files derived from their .svg's, is the best way to give the impression of movement along the arrows to have them lengthening in the direction of travel?

Sorry I can't understand what you are after.
Could you post an example of your work -what you have, and some description of what you want it to be like?